The points D and E are ________.

Two planes intersect at a

Points that lie on the same line are _________.

The scatter plot shows the number of person-to-person e-mail messages sent each year. Make a conjecture that could be true.

We observed the given plot clearly and found the suitable conjecture from the given options.

Write an expression for the nth term in the sequence 3, 5, 7, 9, 11, … and find the value of the 100th term.

While solving the question  we observed how the pattern is changing for different value of n. and then obtained the general equation.

Look at the pattern: 3, 6, 12, 24, 48, ...
Make a rule for the nth term.

We obsrved the pattern with a table how it changed for different value of n. From the table we derived the general equation.

Look at the pattern: 3, 6, 12, 24, 48, ...
What is the next term in the pattern?

In the solution first we found the general equation of the pattern and then found the next term = 96

Look at the pattern 2, 4, 6, 8, 10, ...
Describe the pattern and try and find an equation that works for every term in the pattern.

We observed number in each case and then obtained the general formula working for all the values of n.
General equation = 2n

Determine if this conjecture is true. If not, give a counterexample.
The difference between two negative numbers is a negative number.

Here we verified the above statement with a example. and proved that the statement is incorrect

If it is a number, then it is either positive or negative. What is an appropriate counterexample?

Here in this solution we understood definition of positive, negative. And found the counter example.

If it is an angle, then it is acute. What is an appropriate counterexample?

We understood thhe general definition of acute angle and then eliminated the incorrect option to obtain the correct option

How many squares will be in the 5^th figure?

We observed first four figures carefully and then obtained a relaton to find no of squares in 5th figure = 70

Find the pattern to solve the sequence 2, 4, 7, 11….

So from the above solution we can say that +2,+3,+4... is the correct option

Which is a counterexample of any number divisible by 2 is divisible by 4.

We eliminated the incorrrect options to obtain the correct option

Find the next item in the pattern:
- 3, 6,  - 12, 24, ...

Here we observed the pattern in each stage and obtained a certain result to find the next erm